Let $k$ be a postive integer number . Then $2k^2+1$ and $3k^2+1$ cannot both be square numbers.

Question

Let $k$ be a postive integer number . Then $2k^2+1$ and $3k^2+1$ cannot both be square numbers.

I tried to prove this by supposing one of them is a square number and by substituting the corresponding $k$ value. But I failed to prove it.